Are you positive on the 30-06 Ackley? Type 38 / 44 / 99 rifles are known for having generous chambers that allowed for grit/grime that normally jammed up other rifles.

Is the receiver or barrel marked 30-06? As a sportster?

You are correct on original stocks...for a few bucks more, you can buy an original rifle. Best bet is to use a suitable stock and shoot away.